This master's thesis presents some techniques in statistical genetics to study family relationships. Two individuals can share 0, 1 or 2 alleles for any genetic marker. The larger the number of shared alleles between a pair of individuals across loci, the more likely they are to be closely related. Typical allele-sharing analysis consists of plotting the fraction of loci sharing 2 alleles versus the fraction sharing 0 alleles. Allele sharing analysis also plots the mean and the standard deviation of the number of shared alleles across loci. Studies of relationships are based on the probabilities that the alleles are shared identical by descent, the probabilities depend on the relatedness: monozygotic twins, full-siblings, parent-ospring, avuncular, first cousins, etc. It is possible to infer the type of family relationship of a pair of individuals by using maximum likelihood methods. Moreover, in this project we use tools from the field of compositional data analysis and apply these to allele-sharing analysis and relationship inference. To illustrate these techniques a world-wide database of genetic markers is used.